Baseball and softball bat manufacturers are continually attempting to develop ball bats that exhibit increased durability and improved performance characteristics. Ball bats typically include a handle, a barrel, and a tapered section joining the handle to the barrel. The outer shell of these bats is generally formed from aluminum or another suitable metal, and/or one or more composite materials.
Barrel construction is particularly important in modern bat design. Barrels having a single-wall construction, and more recently, a multi-wall construction, have been developed. Modern ball bats typically include a hollow interior, such that the bats are relatively lightweight and allow a ball player to generate substantial “bat speed” or “swing speed.”
Single-wall bats generally include a single tubular spring in the barrel section. Multi-wall barrels typically include two or more tubular springs, or similar structures, that may be of the same or different material composition, in the barrel section. The tubular springs in these multi-wall bats are typically either in contact with one another, such that they form friction joints, are bonded to one another with weld or bonding adhesive, or are separated from one another forming frictionless joints. If the tubular springs are bonded using a structural adhesive, or other structural bonding material, the barrel is essentially a single-wall construction. U.S. Pat. No. 5,364,095, the disclosure of which is herein incorporated by reference, describes a variety of bats having multi-walled barrel constructions.
It is generally desirable to have a bat barrel that is durable, while also exhibiting optimal performance characteristics. Hollow bats typically exhibit a phenomenon known as the “trampoline effect,” which essentially refers to the rebound velocity of a ball leaving the bat barrel as a result of flexing of the barrel wall(s). Thus, it is desirable to construct a ball bat having a high “trampoline effect,” so that the bat may provide a high rebound velocity to a pitched ball upon contact.
The “trampoline effect” is a direct result of the compression and resulting strain recovery of the barrel. During this process of barrel compression and decompression, energy is transferred to the ball resulting in an effective coefficient of restitution (COR) of the barrel, which is the ratio of the post impact ball velocity to the incident ball velocity (COR=Vpost impact/Vincident). In other words, the “trampoline effect” of the bat improves as the COR of the bat barrel increases.
Multi-walled bats were developed in an effort to increase the amount of acceptable barrel deflection beyond that which is possible in typical single-wall designs. These multi-walled constructions generally provide added barrel deflection, without increasing stresses beyond the material limits of the barrel materials. Accordingly, multi-wall barrels are typically more efficient at transferring energy back to the ball, and the more flexible property of the multi-wall barrel reduces undesirable deflection and deformation in the ball, which is typically made of highly inefficient material.
Additionally, a multi-wall bat differs from a single-wall bat because there is no shear energy transfer through the interface shear control zone(s) (“ISCZ”), i.e., the region(s) between the barrel walls. As a result of strain energy equilibrium, this shear energy, which creates shear deformation in a single-wall barrel, is converted to bending energy in a multi-wall barrel. And since bending deformation is more efficient in transferring energy than is shear deformation, the walls of a multi-wall bat typically exhibit a lower strain energy loss than a single wall design. Thus, multi-wall barrels are generally preferred over single-wall designs for producing efficient bat-ball collision dynamics, or a better “trampoline effect.”
In a single wall bat, a single neutral axis, which is defined as the centroid axis about which all deformation occurs, is present for both radial and axial deformations. The shear stress in the barrel wall is at a maximum, and the bending stress is zero, along this neutral axis. In a multi-wall bat, an additional independent neutral axis results from each ISCZ present, i.e., each wall of a multi-wall barrel includes an independent neutral axis. As the bat barrel is impacted, each barrel wall deforms such that the highest compressive stresses occur radially above (i.e., on the impact side of) the neutral axis, while the highest tensile stresses occur radially below (i.e., on the non-impact side of) the neutral axis.
In general, as the wall thickness or barrel stiffness is increased in a bat barrel, the COR decreases. It is important to maintain a sufficient wall thickness, however, because the durability of the ball bat typically decreases if the wall(s) are too thin. If the barrel wall(s) are too thin, the barrel may be subject to denting, in the case of metal bats, or to progressive material failure, in the case of composite bats. As a result, the performance and lifetime of the bat may be reduced if the barrel wall(s) are not thick enough.
The use of composite materials has become increasingly popular in modern barrel design. The impact and fracture behavior of composite materials is very complex. Structural composite materials do not undergo plastic deformation, like metals, but undergo a series of local fractures resulting in a highly complicated redistribution of stress. When these resultant stresses exceed a predefined limit, ultimate breakdown of the structure occurs. It is very difficult, if not impossible, to accurately predict the initiation and progression of failure in these complex structures based on the behavior of unidirectional laminates in the structure. There is a way, however, to predict the amount of elastic energy that can be stored per unit mass for a particular mode of stressing. This is defined as the specific energy storage, which is the amount of energy that can be stored in a material before the material fails.
The specific energy storage capability of a material for tensile or compression loading is defined as follows:ε=σIt2/EItρwhere                ε=specific energy storage        σIt=ultimate longitudinal tensile (or compressive) strength        EIt=Young's longitudinal tensile (or compressive) modulus        ρ=density        
Thus, a material with high tensile/compressive strength and low modulus and density will have good energy storage properties.
Elastic materials undergo deformation (i.e., spring like behavior) when influenced by the application of a force. Under conditions such as impact loading, when large forces are applied over short periods of time, kinetic energy is transformed at the elastic material interface into potential energy in the form of deformation. As a result of entropy, some irreversible losses, in the form of noise and heat, occur during this energy transfer process.
When the available kinetic energy of impact is transformed into deformation in the elastic material, the elastic material releases this stored energy in the form of kinetic energy back to the impacting body (i.e., the ball), if it is in contact, and/or the stored energy is dissipated within the elastic material, if the impacting body is not in contact with the elastic material. As a result of irreversible energy losses, the elastic material eventually returns to its original stress-free condition.
The total conservation of energy equation for a bat-ball collision is as follows:UK1b+UK2b=UK1a+UK2a+UII+UBM+UMSwhere,                UK1b=ball kinetic energy before impact        UK2b=bat kinetic energy before impact        UK1a=ball kinetic energy after impact        UK2a=bat kinetic energy after impact        UII=local bat and ball strain energy loss        UBM=energy loss associated with bat beam modes        UMS=energy losses associated with heat and noise(Mustone, Timothy J., Sherwood, James, “Using LS-DYNA to Develop a Baseball Bat Performance and Design Tool”, 6th International LS-DYNA Users Conference, Detroit, Mich., Apr. 9-10, 2000).        
Control and optimization of these losses is important to the design of high performance durable ball bats, particularly the losses associated with local bat and ball strain energy. The other losses, such as those associated with heat and noise, although a significant component in the overall equilibrium equation, are minor in comparison to the strain energy losses. Thus, to design a high performance durable bat, it is desirable to minimize strain energy losses in the barrel of the ball bat.